A225162 - OEIS

%I #5 May 01 2013 12:21:01

%S 1,9,91,9181,92480761,9304615055139121,

%T 93529710772930377727152664652641,

%U 9394835719974970982728198049552322910011762062750179997188274881

%N Denominators of the sequence of fractions f(n) defined recursively by f(1) = 10/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.

%C Numerators of the sequence of fractions f(n) is A165428(n+1), hence sum(A165428(i+1)/a(i),i=1..n) = product(A165428(i+1)/a(i),i=1..n) = A165428(n+2)/A225169(n) = A220812(n-1)/A225169(n).

%F a(n) = 10^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.

%F a(n) = 10^(2^(n-2)) - p(n) with a(1) = 1 and p(n) = p(n-1)*a(n-1) with p(1) = 1.

%e f(n) = 10, 10/9, 100/91, 10000/9181, ...

%e 10 + 10/9 = 10 * 10/9 = 100/9; 10 + 10/9 + 100/91 = 10 * 10/9 * 100/91 = 10000/819; ...

%p b:=n->10^(2^(n-2)); # n > 1

%p b(1):=10;

%p p:=proc(n) option remember; p(n-1)*a(n-1); end;

%p p(1):=1;

%p a:=proc(n) option remember; b(n)-p(n); end;

%p a(1):=1;

%p seq(a(i),i=1..8);

%Y Cf. A100441, A165428, A220812, A225169.

%K nonn

%O 1,2

%A _Martin Renner_, Apr 30 2013